Results 161 to 170 of about 224,835 (201)

On Groups with all Subgroups Subnormal

Bulletin of the London Mathematical Society, 1985
It seems to be unknown whether every group G which has all its subgroups subnormal is soluble. Here it is shown that every such group G in which no nontrivial section is perfect, is hyperabelian and hence (by a result of Brookes) soluble.
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On cofactors of subnormal subgroups

Journal of Algebra and Its Applications, 2016
For a soluble finite group [Formula: see text] and a prime [Formula: see text] we let [Formula: see text], [Formula: see text]. We obtain upper bounds for the rank, the nilpotent length, the derived length, and the [Formula: see text]-length of a finite soluble group [Formula: see text] in terms of [Formula: see text] and [Formula: see text].
Monakhov, Victor, Sokhor, Irina
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Coradicals of subnormal subgroups

Algebra and Logic, 1995
IfF is a nonempty formation, then theF-coradical of a finite group G is the intersection of all those normal subgroups N of G for which G / N ∈F. We study the structure of theF-coradical of a group generated by two subnormal subgroups of a finite group.
S. F. Kamornikov, L. A. Shemetkov
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Non-subnormal subgroups of groups

Journal of Pure and Applied Algebra, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Maximal Subgroups of Almost Subnormal Subgroups in Division Rings

Acta Mathematica Vietnamica, 2021
A subgroup \(H\) of \(G\) is called ``almost subnormal'' if there exists a finite sequence of subgroups \(H=H_1 < H_2 < \dots
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On subnormal subgroups of linear groups

Siberian Mathematical Journal, 2008
Summary: We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible.
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On σ-Subnormal Subgroups of Finite Groups

Siberian Mathematical Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kamornikov, S. F., Tyutyanov, V. N.
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NILPOTENT SUBGROUPS OF GROUPS WITH ALL SUBGROUPS SUBNORMAL

Bulletin of the London Mathematical Society, 2003
The main result of this remarkable paper is the following theorem: If \(G\) is a group with all subgroups subnormal and \(S\) is a nilpotent subgroup, then the normal closure \(S^G\) is also nilpotent. It follows from here that a group with all subgroups subnormal is a Fitting group (i.e.
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Chains of Normalizers of Subnormal Subgroups

The American Mathematical Monthly, 2022
William Cocke, I. M. Isaacs, Ryan McCulloch   +2 more
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Direct Products and Defects of Subnormal Subgroups

Journal of the London Mathematical Society, 1988
For any positive integer n, \({\mathfrak X}_ n\) denotes the class of groups G such that \([G,_ nH]=[G,_{n+1}H]\) for every subnormal subgroup H of G. Using Roseblade's Theorem on groups in which every subgroup is subnormal of bounded defect, it is shown that \(G\in {\mathfrak X}_ n\) if and only if \(G\times G\in {\mathfrak B}_ n\) (\({\mathfrak B}_ n\
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